Room 7 of 11 · Upper floor
The Link
“Can two things belong together without becoming one?”
Lamp waiting
▶ Hear the storyteller tell this roomLook
Two rings hang in the air, threaded through each other like links in a chain. They never touch.
Try
Turn the rings. Take a flat picture. Then put the missing dimension back.
Notice
Try the experiment first. Then this will fill in.
What keeps this room working?
The rings stay separate and stay linked.
What would break this room?
If they could be pulled fully apart, or if they melted into one ring.
Child-sized version
“Close does not mean same. Linked does not mean merged.”
Try to break the room
For grown-upsShow me the math
Two fibres of the Hopf fibration are linked exactly like this: any two of its circles thread through each other once, and none of them touch.
- Linking number
- How many times one loop threads through the other. Here it is one.
- Projection
- A flat picture of a shape that lives in three dimensions.
- False crossing
- A crossing that exists only in the flat picture, not in the room.
- Hopf link
- The name for two circles linked once.