# Mathematician Employs Shadows and 3D Printed Sculpture to Help Visualize 4D World

As if we weren’t functioning well enough with high-tech progress in our 2D world, along came 3D design and 3D printing as we outdid ourselves—and continue to do so—with a multitude of inventions and indeed, a new world of technology and a revolution ushering in a new industrial age. That’s not enough though. And as we head into the fourth dimension, science lovers can certainly only give thanks for infinity and the possibilities for a never-ending platform of dimensions. And what innovations will they usher in?

It’s handy to have math and art all rolled into one to try and not only discuss the fourth dimension—but to help us visualize it also. Thankfully, Henry Segerman of Oklahoma State University at Stillwater is both an artist and a mathematician. He makes the topic a bit more clear with general simplicity and the vaguely understandable concept that the third dimension is, in essence, just as impossible as the fourth is, and vice versa.

He demonstrates his fourth dimension like another spoke in a drawing, and it’s really just as simple as that. The question is can we can see it? We cannot, except to ‘squish’ the fourth dimension down into three dimensions, perhaps, which we are evolved to understand and see—or, again, in brilliant simplicity, Segerman shows us the fourth dimension basically as the third dimension’s shadow which is then transitioned away and moved.

He demonstrates one cube inside another, and then begins to explain the hypercube idea which consists of eight cubes as sides. The concept is unwieldy, obviously, so (in the video below) Segerman uses shadows, lights, and different ‘translations’ of the hypercube to try and explain how we can actually think of a fourth dimension without blowing smoke out of our ears.

‘More Fun than a Hypercube of Monkeys’

Showing off not only his talents as a mathematician in explaining spatial and dimensional concepts, we also get to see Segerman take to what many might consider to be an easier and more enjoyable form of viewing the fourth dimension: 3D printed sculpture. Employing his skill as an artist and 3D printing technician, Segerman continues to give us a well-rounded education in the fourth dimension with his humorous display—while also exhibiting some major talent—of the 3D printed hypercube held together by crazed simians tumbling into the much discussed fourth dimension. The sculpture, quite an impressive display both of art and 3D printing, is titled ‘More Fun than a Hypercube of Monkeys.’

The 3D printed sculpture was displayed this weekend in San Jose at The American Association for the Advancement of Science annual meeting, and is also featured on Shapeways.

It seems to me if we can go this far, we should be able to imagine any number of dimensions. The key seems to be in enjoying the visual aspects and not thinking about it too hard—better to leave that work up to the ‘beautiful minds’ of our generation.

What do you think of the concept of the fourth dimension? Is it almost too difficult to conceptualize or ‘see?’ Is Segerman’s sculpture one you like to have on the coffee table? Tell us your thoughts in the 3D Printed Sculpture Helps Visualize 4D World forum over at 3DPB.com.