I think (note: I am not a cutting-edge theoretical physicist) that the brain would work fine against both of these effects.
First, I'm not sure it's possible for the brain to be half-way across an event horizon. When an in-falling object nears the event horizon, the horizon "dimples" in response to the changing gravitational field caused by the object's mass.
Second, once inside the horizon, it is true that messages cannot be sent opposite the direction of the singularity. However, your entire brain is moving toward the singularity, and therefore neural communication does not require messages to be sent away from the singularity.
>Things past the event horizon should be able to travel in the direction of it, though they will always turn back before actually crossing it.
According to the best of my understanding, if you're inside the event horizon, every direction you look leads to singularity. There are no paths away from the singularity.
I'm not sure it's possible for the brain to be half-way across an event horizon.
Sure it is. But the brain is falling inward, so nothing has to move outward across the horizon for the brain to continue working. Everything falls inward, but signals traveling from one part of the brain to another might fall inward slightly more slowly, so the part of the brain the signal is going to will "catch up" with the signal, from a global perspective.
By "a global perspective", I just meant referring the motion of all the objects involved to the global radial "r" coordinate, not to any local inertial frame. I didn't mean to imply that the global perspective was somehow "special", just that it was different.
Not all your brain would be the same distance from the singularity. So when trying to send a signal from a nearer part to a farther part, you are prevented. The brain cannot function.
> Not all your brain would be the same distance from the singularity.
True, but you are not standing still. You are moving. Accelerating, in fact. No messages need to be sent away from the event horizon for the brain to work.
First, I'm not sure it's possible for the brain to be half-way across an event horizon. When an in-falling object nears the event horizon, the horizon "dimples" in response to the changing gravitational field caused by the object's mass.
Second, once inside the horizon, it is true that messages cannot be sent opposite the direction of the singularity. However, your entire brain is moving toward the singularity, and therefore neural communication does not require messages to be sent away from the singularity.
>Things past the event horizon should be able to travel in the direction of it, though they will always turn back before actually crossing it.
According to the best of my understanding, if you're inside the event horizon, every direction you look leads to singularity. There are no paths away from the singularity.