Rod Of Asclepius

On the course of reading about Ophiuchus (my last post.) I came around this symbol:

For the past months or so I've been asking my friends why the sign on ambulances or hospitals is a snake. None of them knew why (probably because I never asked friends in the medicinal field.) I didn't bother researching because....-.- But since I came across this while reading about the new zodiac sign, I found out that this is actually the Rod of Asclepius (god of medicine and healing-Greek mythology.) Interesting.  One other thing I thought about was this symbol:

I see this on some medical stuff too. Maybe it's a pimped out rod for Asclepius! ;-P Turns out it's Caduceus. It's a staff linked to Hermes - messenger of the gods, guide of the dead and protector of merchants, shepherds, gamblers, liars and thieves. So absolutely nothing to do with medicine. I think some hospitals may need to rethink their symbols. ;) Maybe there's something I'm missing. Is it acceptable to use this as a symbol for medicine and healing too? I'm tired of reading. If anyone knows why this 'mistake' is commonly made, tell me about it. Thanks!

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Update: