And yet this advice is not necessarily wrong. We spend a significant fraction of the calories we eat operating our brain. I have personally measured a significant increase in my ability after a good lunch compared to just an hour or two prior.

Yes, this is my intended meaning. I am a PhD student working on my thesis. After a certain number of hours of doing mathematics or algorithm design, I have to switch to easier tasks like reading papers in a domain I'm familiar with, or documenting code.

While I cannot speak for anyone but myself, my performance on highly challenging tasks is capped at 4-5 hours per day. At that point, it is better for me to switch to lower hanging fruit.

If I am feeling especially inspired, sometimes I'll put in a 12+ hour day of hard work. Rarely, even two or more in a row. But inevitably, I will feel extra burned out in the subsequent days.