Overall, there’s only limited evidence for thinking hard using more calories. You don’t burn a lot less energy for example when you’re sleeping compared to when you’re awake. I’d argue that when you’re sleeping you’re dealing with a lot of difficult problems as well.
So, actually, it’s not a net thing. And once you’re good at hard problems you use less energy than the first time you did it. Once you become an expert in solving very difficult problems there is evidence that you use less energy in those particular areas of the brain than you used first time around.
https://www.youtube.com/embed/dHh5VCx3m-Y?wmode=opaque
Therefore, it’s not a simple relationship between thinking hard and energy consumption. Although it does sometimes work that way.
"Brain energy techniques don’t look at neural activity directly, but rather they look at the distribution of oxygen in the brain"
Different tasks do have a different energy load on the brain. Brain energy techniques don’t look at neural activity directly, but rather they look at the distribution of oxygen in the brain. The reason why you can see different distributions of oxygen in the brain when different bits of the brain are more active is because they need more energy - they need more oxygen. So the blood supply to those small areas that are responsible for, let’s say seeing lines moving to the left rather than the right, does cause energy consumption difference locally.
https://www.youtube.com/embed/9UukcdU258A?wmode=opaque
The question of whether there’s a global difference in the energy consumption of the brain is harder to find evidence for, because what’s happening is compensation where blood is being shunted from one part of the brain to another. So most of the difference in energy consumption is local, not global.
Some might think sitting in front of the TV is resting your brain but when your eyes are open in front of the TV and there are brightly flickering images it generates a lot of activity in the visual cortex. There’s a lot of interest in what we call the ‘resting brain’ - and it should be put in quotation marks because what the brain is doing is processing that is less driven by external inputs. But there’s good evidence that you process a lot of information in your sleep for example.
"It’s certainly not the case that you shut down the brain when you are resting"
It’s certainly not the case that you shut down the brain when you are resting. There are differences in energy consumption, and certainly locally but whether there is a global difference is not clear.
The only exceptions to that are if you’re in an induced coma or indeed if you have a traumatic brain injury, then processing does slow down or even shut down.