There is masses of scientific research into work patterns; and it's pretty conclusive that to be effective, you need a minimum of one hour "off" at midday. That means totally switching off. Whether you are doing physical work, using machinery, or doing desk work.
We researched loads of papers, and did our own research into this as part of a study for MOD, looking at the most effective patterns for work/rest, especially under stress conditions.
Working through lunch break massively reduces ability to do error free calculations, ability to make decisions, ability to problem solve, and increases stress. Can be as much as 25-50% reduction.
It's actually one of the reasons cited for UK's poor productivity; longer hours, fewer breaks. Per man hour/ lab-week, countries like France which retain the long lunch hour are far more productive. And there is also less conflict and more job satisfaction . And anecdotally, in a "problem solving/analysis" office, it was easy to see that those who took longer lunches, and who got up and walked off for a coffee, or a fag, or just a walk or a social chat for 10 minutes every so often, got through more work, and were more creative than those who adopted the " lunch is for wimps" philosophy.
For myself, as the department leader, I had offices and labs all over our site, so I got my "breaks" by making sure that I spent a lot of time doing "MBWA" - Management by walking about- visiting each group or team for a few minutes everyday.
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