The original note, as written at the time
A space station with rotation capability for gravity. The rotating cylinder comprises a number of rotating rings. Let us say it comprises 10 rings numbered from one end of the cylinder to the other. If the odd rings rotate clockwise, the even rings rotate anticlockwise. The important concern here is to make sure the rotational radius is the same for all the rings.
Ongoing development
A space station with rotation for gravity, built as a cylinder of numbered rings: odd rings turning clockwise, even rings turning anticlockwise, and every ring at the same radius.
The counter-rotation is the design’s real content. A spinning habitat stores angular momentum, and a stored momentum has to be managed — every movement of mass inside it, every docking, every crew walking in a circle, pushes against it. Splitting the rotation into alternating rings cancels the net momentum, so the station does not need thrusters fighting itself forever.
The equal radius is the compromise the arrangement forces. If the rings alternate, they cannot be nested without giving up the same share of gravity, so the whole cylinder must present one inner surface — which means the transfer between rings is the hard part, and a person crossing from a clockwise ring to an anticlockwise one has to change their own motion.
That is the detail that makes it architecture rather than a diagram. The interface between two rings is a moving joint with an atmosphere on one side, and it is where every proposal of this kind dies.
The interior gains a strange quality: a continuous floor, a curved horizon, and a visible rotation of the sky that alternates direction as you walk. That is a place with an entirely new kind of weather and nobody has written about what it does to people.
Build the joint first. Everything else in the station is a cylinder, and cylinders are easy.