If I'm cutting pulpwood or stacking boxes in a warehouse, it doesn't really matter whether my brain is engaged or not; it's mechanical labor and damn near mindless anyway[1]. But if I'm writing code and solving problems, and my brain isn't in gear, I can come sit at the desk for eight hours, but I'm not going to get anything accomplished, except building resentment for having to sit there at the desk for eight hours and look busy.

[1] Perversely, I miss burning wood; as a kid I cursed the woodpile, but its good exercise and you can get a lot of thinking done while you do it.