Creepy Shadows

I think the part of the video below I’m going to suggest you watch is creepy in a subtle way. This might just be me and my over active imagination, but it might not. The video is of a talk given by Matt Parker, a Mathmetician, to a group of children at the Royal Institution. The talk is about Geometry and is light hearted and fun. I don’t know if this talk is one of the RI’s Christmas lectures, but Parker is stood at Farady’s desk.

At about forty minutes in, the talk becomes sinister.

Parker shows an animation of the shadow of a cube unfolding into its net. Think of the lid of a square box flipping up, the back-side dropping down, and the sides collapsing, and you’ll get the idea. Then, he shows an animation of a 3D cube unfolding under a light to explain the first animation of the shadow. All good so far.

Then, keeping to exactly the same principles as used for a 3D cube folding/unfolding, he plays an animation of the shadow of a 4D net folding itself up to become a four-dimensional cube. This is where the creepy thing happens.

Scroll the video to about 40 minutes in.

As the shadow of the 3D cube’s “lid” flips over, you’ll see the sides “stretch” as it flips. This is okay because we know, instinctively, why this happens because we know about shadows and how they seem to stretch depending on the angle of the light source, and the angle changes because the lid is moving. We understand, and can imagine the movement required to create this “stretch” effect.

But watch the video of the 4D cube, folding and unfolding, and look at how the lid of that shape stretches. It stretches in a way whick looks impossible in 3D – just as the shadow of the lid of the 3D cube looks like it stretches impossibly when the 2D shadow moves. What on earth is that 4D cubing doing to cast a shadow like that?

What is that 4D cube doing?

That’s the creepy thing. We don’t know, and can’t imagine it. The unknown is scary.

And if, like me, you have read The Dreams in the Witch House by H P Lovecraft, you’ll know that even a bit of geometry can be creepy.

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