You have two friends: Alice and Bob. Suppose you have a way to remove a healthy neuron from Alice's brain and conserve it in some safe place. And, viceversa, suppose you have a way to graft this neuron in a certain region of Bob's brain (assuming the new neuron will develop connections with the others nearby).
Then keep repeating the following two steps:
- remove one neuron from Alice and another from Bob, both possibly from the same region;
- graft Alice's neuron in Bob's brain and viceversa (again, both in the same region)
until all neurons have been exchanged.
After we have exchanged all the neurons, will Alice and Bob still feel the same? If so, consider this: let
v be the speed at which we complete the entire operation, with
v = 1 meaning instant exchange and
v = 0 meaning infinite time (no exhange at all). What would be the maximum possible value of
v such that Bob and Alice still feel the same after the operation?