Quote: "it's weird that it wasn't invented earlier by mathematicians before electricity was around. "
Indeed! I can affirm that a string computer is indeed mathematically possible with my gate design. It's impractical, however, simply due to friction. About two years ago, when I was first trying to come up with a design for a string logic gate, I came up with many designs that were unsatisfactory to me. They included things like springs or weights. Such gates are severely limited in how much force they can output; perhaps both inputs would be in the low position, but you could hold the output in the high position with enough force (which wasn't much, just enough force to overcome the weight/tension of the weight/spring). By extension those gate are severely limited in how many other gates they can drive.
With my design, the output
will be in the high position if both inputs are high, and otherwise, it
will be in the low position, unless the gate has been damaged.
All of the force used to move it is derived from the inputs, and not from weights/springs.
So yeah, because the force used to move an output comes from the inputs, the amount of force required to actuate an entire logic circuit builds up really fast as gates connect. If it takes 5 newtons of force to actuate one gate, my XOR gate there could take up to 15 newtons of force to actuate.
If I had pulleys, I could reduce all of the sliding friction to rolling friction, which would be excellent.
