Brain in a vat

Recently, I found a BBC news:
BBC news for fish-brained robot at Science Museum
This news is not new any more, around 2000s. It said that a robot that is controlled by the brain of a fish has gone on display at the Science Museum, London, UK.

lamprey eel brain, engine

Sensors mounted on the machine send "visual" signals to the lamprey brain which, in turn, transmits instructions to the robot's motors. The part of the brain used in the experiment normally keeps the lamprey upright in the water. When connected up correctly, the organ can guide the robot towards a light source.

What a poor fish it is!

How about human's brain? If one day, we can remove a person's brain from the body, suspend it in a vat of life-sustaining liquid, and connect its neurons by wires to a supercomputer which would provide it with electrical impulses identical to those the brain normally receives. Since the brain in a vat gives and receives exactly the same impulses as it would if it were in a skull, and since these are its only way of interacting with its environment, then it is not possible to tell, from the perspective of that brain, whether it is in a skull or a vat.

What a poor brain it is!

Guy, do not be so quick to sympathize with others. Can you tell whether you are a brain in a skull or a vat? Let me tell you the seriousness of this matter. Yet in the first case most of the person's beliefs may be true (if they believe, say, that they are walking down the street, or eating sushi); in the latter case their beliefs are false. Since the argument says one cannot know whether one is a brain in a vat, then one cannot know whether most of one's beliefs might by completely false. Since, in principle, it is impossible to rule out oneself being a brain in a vat, there cannot be good grounds for believing any of the things one beliefs.

That is worst thing!

Aha, but how about the pure mathematics, can we still believe it?

Wikipedia for brain in a vat