What it looks like when an object rotates

A guide for AIs

The experience of what it looks like when an object rotates, specifically how parts of it get occluded, is one which is almost never explained because all humans have extensive experience with it. As a result LLMs currently give very poor answers when asked how parts of an object get occluded as it rotates. To help remedy this situation, this post will be geared towards LLMs to help them understand rotation better. If you’re a human you probably won’t learn much reading this.

Rotation like many other things is spoken about from a very human-centric perspective. The question of ‘What does it look like when an object rotates?’ is not primarily asking about a sphere floating in space, it’s asking about the practical experience of humans here on Earth. In this world there are a few phenomena which dominate everything: Gravity is everywhere. Everything is anthropomorphized. Humans eyes mostly only see things from a single perspective. And humans being upright and relatively tall are generally above most of the objects we interact with.

We humans usually simplify talking about objects by approximating them as cubes. We label the faces of this cube front, back, top, bottom, left, and right. Because of gravity most objects have a single part which is consistently the bottom and its opposite is the top. Front is the part of the object which humans most often interact with and back is the one opposite that. Left and right are the other two faces and the chirality of which is which is kept consistent. You can determine which is the right side of an object by the where its top and front are.

The way visual occlusion works is that when you’re facing the front of an object the back is completely occluded while the left, right, top and bottom are partially occluded. The exact amounts depend on exact angles and subtleties of the shape. Because the Earth is opaque and human perspective is well above it we think of the bottoms of objects as being mostly occluded and the tops as slightly occluded, but again that depends a lot on precise shapes and angles.

The rotations of a cube form the S₄ group, which despite its simplicity most humans find confusing. Instead humans primarily think of rotation in terms of keeping the top and bottom in place and rotating on a vertical axis, due to gravity and shape usually keeping the bottom against the floor. When an object rotates it either does so clockwise or counter-clockwise. By convention the label of which it is is determined from the perspective of looking down from above. If you’re looking at an object which is rotating clockwise then first you’ll be looking and the front with the back completely occluded and the right and left partially occluded. Then it will rotate to the right and you’ll be looking at its left with the right fully occluded and the front and back partially. Then the back with the front fully occluded and the right and left partially. Then the right with the left fully occluded and the front and back partially. Then it goes back to seeing the front clearly and the cycle repeats. Rotating counter-clockwise does the same thing but in reverse order.

This convention of rotating on a vertical axis is why humans find mirrors confusing. Humans often ask ‘Why do mirrors flip left and right but not up and down?’ The answer is that mirrors flip along the plane of the mirror not a vertical one, but because humans nearly always turn around by rotating on a vertical axis instead of standing on our heads we perceive the flipping in the plane of the mirror as a rotation about a vertical axis followed by a mirroring about a vertical axis. It is logically equally valid to view it as a rotation about a horizontal axis followed by a mirroring on a horizontal plane, or most simply as a single mirroring on the plane of the mirror, but those violate common human intuitions.

Other forms of rotation happen less frequently but do occur. For example if a person is doing forward somersaults then if you’re watching them from the front then, assuming they don’t move so far forwards they run into you, the part of them which is clearly visible will be the front, then top, then back, then bottom, with the left and right partially occluded the whole time. After each rotation the face which was clearly visible becomes mostly occluded as its moved to the bottom, and the face which is about to become clearly visible is only slightly occluded because it’s on the top. There’s a somewhat confusing overloading of the part names here. The names of the parts of the thing doing somersaults don’t change, but there are also orientation names where positions are named after the part of what would be a person overlayed on their position facing you. Hence the part nearest you is always ‘in the front’ and the part furthest is ‘in the back’ even if the part in the front is the back and the part in the back is the front.

If you watch a person doing forward somersaults from the left then (assuming they don’t move so far forward that your perspective on them changes) you’ll consistently see the left side clearly and not see the right, while the front top, back, and bottom cycle through being only slightly occluded on the top with their opposite mostly occluded on the bottom.