Fourth dimension for skeptics

Gotta share this. I did a mind bending experiment the other day. I was playing around with the shadow tree sculpture and came with the odd idea to replace the white LED at its center by a green and a red led.

The Shadow Tree
[image credit and 3D printed by @printabit]

As expected this created two overlapping shadows with green and red edges.Then I put on a pair of coloured 3D glasses and the strangest thing happened: the shadows came off the wall! The shadows of the shadow tree were in the room, floating in front of me like a ghostly deceased tree. There wasn’t enough light to take a photo but if you happen to have red-green glasses (as opposed to red-cyan), here is a rendered version of the shadows.

red green shadows: a real world anaglyph

Now, some of you will know about my obsession with dimensions. In this post I argued that your eyes give you a 2.5D view of an otherwise higher dimensional reality. I even tried to give you a 4D experience. For most, that was a fail. Now, I have a better experiment for you – and more fun!

Meet the Tesseract. A tesseract is a 4-dimensional cube. When you look at it from a 3D perspective, it makes no sense. Look at this rotating in 4D. Confused? Of course you are.

Rotating tesseract
[image credit Wikimedia]

Make your own Tesseract

But we can do better. Using the idea of red-cyan anaglyphs, we can make a real tesseract. It is time to get your updated pre-school toolkit out: paper, scissors, glue and color printer. Here are the instructions:

1. Print out the pdf of the tesseract (like the image below). Your printer may mess up the colors a little (mine did) but it should still work;
2. Cut out the tesseract along the dotted line;
3. Trace the fold lines with the back of a knife to ease the folding;
4. Fold the tesseract into a cube and stick the folded lips together with paper glue.

Click for PDF

Done. You should end up with something like the cube in the photo at the top of this post.

Now, here is the challenging part: you need to get a pair of red-cyan glasses. They used to come with 3D videos for kids. I dug deep and found an old pair of Barbie glasses. God bless Barbie. You’ll have to look in similar places and if you ask anyone with kids that are now teenagers (if only they still watched Barbie!), then chances are, there are red-cyan glasses to be found.

Put them on and marvel. You’ll see a cube within a cube. If it protrudes instead, turn the cube upside down. And as you rotate it, you are getting view of a four dimensional tesseract. This is seriously geek cool.

Your brain may protest. Let it. Four dimensional objects are both a mathematical and physical reality. Because we have been conditioned to think that we can only observe three dimensions, we are tempted to dismiss experiments like this. The reality is that we can see and have seen instances of four dimensions but we didn’t recognize them as such.

Now sadly, there is no way to show four dimensional images on a two dimensional blog post. You have to do the printing, cutting and gluing. It took  me 10 minutes in all. Four dimensions have to be experienced to be understood. Like sex, lemon juice and falling of cliffs; it isn’t enough to imagine it.

Enjoy 🙂