The original mentioned, Arthur Ganson's Machine with Concrete, is quite a bit more artistic. The end is cast in concrete.
The idea is that there is a certain amount of energy lost as friction in each gear, per turn. If you calculate the gear ratios and how many turns of the earlier gears would be required to make the final gear move, even infinitesimally, the amount of energy lost becomes more than all the energy in the known universe. It's not really about RPMs.
It's also the elastic modulus of the gears. Every solid thing has some stiffness or measure of how much it compresses/stretches when it's loaded.
There will be finite (but extremely small) compressive/tensile forces that are absorbed in the stretch of the material that the gears and driveline are made out of.
Like stretching a rubber band to double its length takes a force you can feel but stretching it 1/100 of that (or one one millionth or lower) takes effort you don't even notice.
The OP's gears are better laid out to illustrate the concept, and they let you think about what happens with the last gear instead of demonstrating it so... concretely.
Even without that, even 50 of these gears would take the mass-energy of something between a star system and a galaxy cluster to turn at any human-scale timeframe
When all the slack has been rotated out, it would require a tremendous amount of force to rotate that last gear in reverse. After all, the system wants to amplify the gear speed from that end.
I think parent’s idea would work if the system was mirrored and duplicated. Then you could attach the two the them together with the stationary gears in the middle
Actually not mirrored, just duplicated and joined at the concrete face. Mirrored would rotate in the same direction. Then it’ll “create two universe worth of energy” at the center of it.
So 10^100:1:10^100? I think the slack, friction losses, flex, material strength would all take out so much of the energy you'd get a tiny fraction of movement at the far end if any.
The idea is that there is a certain amount of energy lost as friction in each gear, per turn. If you calculate the gear ratios and how many turns of the earlier gears would be required to make the final gear move, even infinitesimally, the amount of energy lost becomes more than all the energy in the known universe. It's not really about RPMs.