Conscious experience is evidence that the brain doesn't something we have no idea how to compute. One could argue that computation is an abstraction from collective experience, in which the conscious qualities of experiences are removed in order to mathematize the world, so we can make computable models.
If it can't be shown, then doesn't that strongly suggest that consciousness isn't computable? I'm not saying it isn't correlated with the equivalent of computational processes in the brain, but that's not the same thing as there being a computation for consciousness itself. If there was, it could in principle be shown.
