Jake Herridge

From Where You Stand

Every view is true. None is complete.

One room, one clock. Every box below shows the same shape at the same moment. Real spins, real shadows, real slices, and a shutter you control. The math runs live, right now. Nothing is a video.

One shape, every view

Pick a shape. All four boxes below watch the same shape at the same moment. Box one draws it flat on this page. Box two is its shadow. Box three is only how wide the shadow is. Box four is a dot.

The tesseract, flattened twice to fit this page. 4D → 3D → 2D.
Its shadow, straight down. A shadow of a shadow. 4D → 2D.
The shadow's width. All a 1D eye would see. 4D → 1D.
0D. It is here.

The shutter

The shape spins at one speed. You watch at your own speed. A camera does not see motion as a flow. It takes quick peeks, one after another. Time the peeks just right and the spin looks frozen. Peek a little faster and it seems to run backwards. The shape never changes speed. Only the looking changes. This one shutter runs the whole room, slices and game included. Wagon wheels in old western movies do this same trick.

Through the paper

Picture a world as flat as paper. It cannot see a whole cube. It only sees the thin slice passing through it. This page is that flat world. The same trick works on us, one floor up. When a 4D shape passes through our world, all we see is a 3D slice that grows, changes, and disappears.

A cube sinking through the paper. Left: what we see. Right: all the flat world gets. Corner first, the middle slice is a perfect hexagon.
It is not in our world right now.
A tesseract sinking through our world. This is all we ever get to see of it. Cube first, it looks like a plain cube the whole way, then it is gone. Corner first, the middle slice is a perfect octahedron: eight triangle faces.

From one angle

Five hidden shapes, one at a time. You get one view of each. Guess what it is. Another person stands off to the side, ninety degrees away. Ask, and they will tell you what they see.

Round 1 of 5
From where you stand.
From where they stand.
The object, both views attached.

Every view was true. None was complete.