Hopf fibration

Okay, so imagine you have a ball. If you take a string and tie one end to a point on the ball and then stretch the string out so it's straight, you can move the other end around the ball in circles.

Now imagine you have a second ball, and you tie that string to a different point on the second ball. You can also move the other end of that string around the ball in circles.

But what happens if you tie the ends of those two strings together?

Well, something interesting happens! The two balls become connected in a very special way that is called the Hopf fibration.

The two balls are now linked together, but not in the way you might expect. Instead of being linked like two rings or two circles, they are linked in a way that is kind of like a spiral.

It's kind of like if you had a spiral staircase that went around two different buildings. They are linked together, but they don't touch each other directly.

That's what the Hopf fibration is all about. It's a special way that two balls can be linked together using circles and spirals. And scientists and mathematicians study it to learn more about how things can be connected in different ways.