There are 7 extra dimensions in some versions of hyperstring theory. Other numbers are possible, even as many as 24 or so but analysis bogs down the machines. The extra dimensions are invisible to us because they are very tiny and operate only on subatomic size regions. However, a scientist, I don't remember her name, thinks that one or more of the extra dimensions are somewhat larger in our 3-D space and can be measured in the lab, which she and others are now trying to do. The size expected is a millimeter or so, which would be the size of neuronal groups, so the brain could interact with something, another brain or nervous system, through another dimension. All hypothetical at this time, but could become scientific knowledge if this works out. It would cause a revolution in Galilean science.
Hmmmmmmm.... Maybe the reason that they are invisible to us is not because they're [it's] so tiny, but because they're [it's] so vast? Grandpierre suggests that neurons per se cannot be the mediators of a brain interacting with another brain or nervous system, simply because they are "too large" to be the material carriers of such transmissions. The same holds for cells, molecules, and even atoms. What we're looking for is to be found at least at subatomic, but more likely, at particle/wave levels. Does multistring theory suggest that a teensy little "time window" (extra dimension) must open up to enable wave propagation, and then must close again -- disappear -- once that process is complete? Seems like doing things "the hard way" to me. Kinda kludgey!
But I really don't know; as you say, all this is hypothetical at this point. But I agree with you: a revolution in Galilean science could ensue any time now. We just don't know what that looks like yet!
Thank you so much for writing, RightWhale.