Possibility of increasing brain speed In science fiction stories, we often see the use of virtual reality, a 3d world that allows you to actually 'be' there. The writers often use a pod or helmet to signify the use of some sort of computer that reads and sends information to the brain. What many, if not all, of them have in common is that time is sped up. If it isn't double then it's triple or much more. Now, while this is science fiction and far removed from any real basis, I'm curious. Is it possible to speed up brain in such cases? I.e. Would we be able to make time move faster in a virtual space?

My gut, deduction, and the meagre amount of information I found online, says it's impossible. I know very little about the brain, but processing information at a much faster speed would force a much bigger strain on the organ, thus overtaxing it. Not to mention, if the brain could actually run faster, wouldn't it have it's own mechanisms for running faster, considering it would be quite the advantage when you want to survive as a cavemen against a lion that's in need of some breakfast.
There are just too many ways to answer this question. But I suspect all of them will be proxies to the ultimate answer - the goldilocks principle.

To give an example, for the human brain to be faster, it would either have to be smaller, or would consume more energy. There is an optimal balance between the size of the brain and its energy ratio (to the rest of the body). Like many factors, these were heavily shaped by evolution (which in turn is heavily affected by our environment).

You can also argue that a faster brain will accumulate processing residues faster, thus we'll have to sleep more frequently, which may have adverse effect on survival chances. I know it sounds far-fetched, but you can actually argue that the size of the brain is correlated to the distance of earth from the sun. That's the goldilocks principle for you. 

Would strongly recommend:

What is so special about the human brain? (TED Talk)

And the first chapter in:

Gibb, B., 2012. The Rough Guide to the Brain, 2 edition. ed. Rough Guides, London.