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From a math perspective, it seems obvious that the electric field (or voltage which ever) of a bit in a computer, when its in a stable 0, or 1 state, must have a singularity, a set of points where the partial derivative is 0 in each direction. From a dynamical systems perspective this is the defining characteristic of an asymptotically stable system.

My question is what is the topological type of this singularity in modern semi-conductor devices. Is it a point, a sphere, a ball? it could be a circle (through the feedback loop), or a torus or a filled torus (again through the feedback loop). Those are all the cases that seem reasonable from the symmetry of the situation. My guess is that its at least a sphere, and probably a torus, because these most respect the symmetry of the problem using the least energy (the filled in sphere, or ball, and filled in torus, would seem to use up a lot of energy). But, I don't actually know.

Is there any one here who does?

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    $\begingroup$ are you referring to a bit flowing through a connection, like a wire, or a bit stored in a flip-flop or RAM circuit? Or a bit stored on a hard drive or other physical drive? $\endgroup$ – Jim Dec 9 '14 at 17:01
  • $\begingroup$ I'm thinking in particular of the bits in a register in the cpu. Magnetic systems are clearly different -- they don't depend on feed back to maintain their state. I assume, possibly incorrectly, that bits in RAM are effectively the same topologically as in a register in the CPU, but too that might be technology dependent. $\endgroup$ – Michael Cloud Dec 9 '14 at 17:23

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