I've been on
I don't think it's quite that simple for everyone. I've been through periods of eating really badly (high fat takeaway for lunch every day for weeks on end) and then really healthy, with identical exercise level (~none), and my weight never moved outside the 69-71kg range that i seem to have been stuck at for the last 5-10 years. I've added up the calories I intake vs the exercise I do (next to none) and by all calculations I should be a balloon. 69-71kg would be about right for my height if there was a bit more muscle on me.
If I don't eat very regularly (eg breakfast at 8am, i'll need something fairly substantial by 10am) I get the shakes and start feeling really really spaced out and crave sugar. If I continue to not eat it kind of settles down and I start feeling a bit normal again but a few hours later i'll get a horrible headache that won't go away for days even with painkillers (although something with a lot of caffeine helps at bit if it goes that far). I've been tested for diabetes and hypoglycemia several times over the years and nothing has showed anything out of the ordinary... i assume i'm just a bit more sensitive to small drops in blood sugar levels than most people.
I know when I'm on a low carb diet, I go through this same process. I've learned that your body naturally processes carbs first (carbs are the only thing saliva starts breaking down carbs as soon as you start chewing). It's easy for the human body to use carbs since they are already close to being glucose.
On a higher carb diet, your body is use to processing carbs, so when you stop eating them every 3-4 hours, it starts to crave them because it needs the energy. On the other hand, when on a low carb diet your body is working to breakdown fat, so the cravings for carbs diminish.
As far as the headaches go, almost everything your body is use to having put it, when removed, will cause a headache. Your body is a giant chemical reaction burning oxygen. Everything you put into it fuels that reaction. Have you ever noticed how the flame of a fire looks different depending on the material burning? That's your body, change what's burning, you get a different reaction...
Mathematicians stand on each other's shoulders. -- Gauss