The brain can live on ketone bodies which are the byproduct of breaking down fat. This is a normal process developed over the eons and the reason you HAVE fat; to get your body and the brain through periods of no food, or only meat and fat intake.
You can also go into ketosis from a diabetic process but this is a disease process and not a healthy normal one.
It's actually quite fun to experiment with; eat no carbs for about two days and once your stored liver glucose, glycogen, is used up, you switch over to fat burning. It's subtle at first but then you feel a burst of energy and get a bit high too; the ketone bodies are a lot like alcohol. It's a very steady-state burning of fuel also, so you cease to be hungry; the ketosis also takes away a spurious appetite; you'll still get hungry but it's easy to think carefully about what you want to eat and take your time cooking it; snacking on anything quickly available isn't as likely.
Whether sustained ketosis can kill cancer cells is still up for grabs, but I'm trying it myself right now. I was diagnosed with breast cancer a few weeks ago and I switched out my diet to more veggies, numerous supplements and I'm trying to avoid blatant carbs. I know I feel better emotionally on the vegetables and avoiding wheat and sugar especially. I'm beginning to think wheat is as much a poison as sugar is, especially in American quantities.
edit on 10-3-2013 by signalfire because: can't spell late at night