The ladder sees the carage length contract. That is less than 10 feet. The ladder doesn't see itself contract that puts the limit on the repeating of the universe.

Are you sure the ladder point equivalences are not (0 ft, 0ns) and (20 ft, -8.8ns)?

Actually from the point of view of the ladder the universe still repeats at every ten feet. It is just that from it's point of view it takes the space of two carages at any one instant.Both the garage and ladder are in a state of rest and show equally good times. Yes they read different but doesn't mean they are in error.

I am not sure whether it would see other instances of itself. I only spesified a spatial gluing and not that the garage be split into timeslices. I guess that the change of the point of view has changed some of that gluing to be from future to past. For if the ladder would be too long the frontend would not crash to the same ladder time backend but to a future one. (ignoring the problem of how you would try to slide the ladder into too small a hole in the first place)

ah, I meant to glue the end and start together without curved shape/motion. But I guess that is physically unrealisable and potentially more distracting than explanatory.

If the ladder point of view is ildefined so is the garage point of view as the front and back of the garage have distinct reference frames. Any inertial reference frame is equally good. The ladder is not accelerating thus inertial. In the sense that we can talk of any frame as more than a single event or world line the ladder frame is perfectly good.

I was thinking of already spun cylinder and then adding the sticks by accelerating them to place.

If you had the same sticks already in place the stick would feel a stretch. If they resist this stretch they will pull apart so there will be bigger gaps between them. For separate measuring sticks they have no tensile strenght in the gaps between them. However if you had a measuring rope with continous tensile strenght and at a beginning / end point where the start would be fixed but new rope could freely be pulled from the end point you would see the numbers increase (much like waist measurements when getting fatter). However the purpoted cylinder has maximum tensile strenght anywhere continously. Thus that strenght would actually work against the rotating force making it resist rotation. a non-rigid body will rupture and start to look like a star.

So no there would not be duplicate sticks but yes the rope would know to engage number 78.

If you would fill up a rotating cylinder with sticks and spin it down the stick would press against each other crushing to a smaller lenght. A measuring rope with a small pull to accept loose rope would reel in. A non-rigid body slowing down would spit-out material in bursts that might come resemble volcanoes.

Every computation requires something that instatiates it, ie a abstract or concrete machine to run on. In a very extreme case you might come up with a very abstract idea. However then the instation provider is the imaginer. Every bit of information requires a transfer of energy. Instation is transitive relation. If there is simulation of me it neccesarily instanties my thoughts too.

Also the parent comment implies a belief in panpsychisism.

Why have that definition of "fit"? I could eqaully well say that fitting means that there is a reference frame that has a time where the ladder is completely inside.

If you had the carage loop back so that the end would be glued to the start you could still spin the ladder inside it. From the point of the ladder it would appear to need to pass the garage multiple times to oene fit ladder lenght but from the outside it would appear as if the ladder fits within one loop completely. With either perspective the one garage space enough to contain the ladder without collisions. In this way it most definetly fits. Usually garages are thought to be space-limited but not time limited. Thus the eating of the time-dimension is a perfectly valid way of staying within the spatial limits.

edit: actually there is a godo reazson to priviledge the rest frame oft he garage as the one that count as ragardst to fitting as then all of the fitting happens within its space and time.

Place red and white equilength rulers on the edge of the cylinder. The rotating cylinder will have more and shorther rulers. Thus the photos are not the same. Even better have the cylinder slowly pulse in different colors. The edges will pulse more slowly thus not being in synch with the center.

Related phenomenon is that moving ladders fit into garages that stationary ones would not.