You also need temporal resolution: when a signal hits the synapse #3489, what will be the exact state of that synapse? The state determines how and when the signal will be passed on. And when the potential from that input goes down the dendritic tree and passes by the synapse #9871, which is receiving an input at that precise moment - well, how is it going to affect synapse #9871, and what is the state of synaps #9871 at that precise moment?
How much of this do we actually need in practice? Humans can be put in states where there's almost no brain activity, such as an induced coma, and brought out of it with no damage. That suggests that things like the precise state of #9871 at that moment shouldn't matter that much.
All of it! Coma is not a state where temporal resolution is lost!
You can silence or deactivate neurons in thousands of ways, by altering one or more signaling pathways within the cells, or by blocking a certain channel. The signaling slows down, but it doesn't stop. Stop it, and you kill the cell within a few minutes; and even if you restart things, signaling no longer works the way it did before.
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