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The Housea dollhouse with rules

0 of 11 lamps lit.

Room 7 of 11 · Upper floor

The Link

“Can two things belong together without becoming one?”

Look

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.

The full statement, through the looking glass →