Plato’s 4D cave

A colleague recently told me about a dream she’d had. She was in VR and somebody showed her a mug and asked her whether it was a real object. Her response was, essentially, no.

Then he showed the same mug to a virtual A.I. in the VR world, and asked her the same question. The A.I. said “sure it is!” and promptly picked up the mug.

I told my colleague that her dream reminded me of thoughts I’ve had about the VR visualizations of four dimensional objects that we’ve been doing in our lab at NYU. We’re doing our best to create intuitive ways for people to rotate and otherwise interact with these 4D objects.

Suppose you were to ask me, while I am wearing the VR headset, whether the thing I am looking at, floating in the air before me, looks like a 4D object. My likely response would be “sure it does!”

But if an actual four dimensional being were looking in on our little exercise, I suspect her reaction would be quite different. “Of course not!” she would likely say. “That’s just a shadow of a 4D object, projected onto your flat little 3D world.”

To such a being, everyone and everything in our Universe is a mere shadow, projected on to a higher dimensional version of the wall of Plato’s cave.

Leave a Reply