A neuron in the brain is subject to orders of magnitude more noise, from chaotic factors like blood oxygenation, signaling molecules, aging...
For our actual conscious experience though, there's some evidence that we're very noise tolerant. I can't find the paper now, but one recently just came out showing that at certain parts of the brain you won't even notice an electric shock.
For our actual conscious experience though, there's some evidence that we're very noise tolerant. I can't find the paper now, but one recently just came out showing that at certain parts of the brain you won't even notice an electric shock.