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xkcd #2846: Daylight Saving Choice
(imgs.xkcd.com)
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I would say not much different from looking up whether they are in the +0530 or +0630 part of India. I guess the perception of convenience also depends on what you are used to seeing.
But no matter which one they're in, you know that by calling at 11 local (no matter if you're using the right time zone) you'll be calling during business hours, no need to check "What are normal business hours in India?"
There's always one check in that situation. Whether it's business hours or timezone difference. And you still need to check business hours even in our current system, so might as well just simplify it (which of course isn't happening any time soon).
Better yet let business hours be based on daylight, no need to wonder if things are open or not based on the sun's position in the sky.
So... Current system then?
Noon is mid day or coffee to it no matter where you are, you know businesses will be open for sure a couple hours before and after noon local time.
No? It shifts midday around. The day gets shorter on both sides of the sun's peak you know?